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# Medical Statistics Part-I:Descriptive statistics

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• Descriptive Statistics

Descriptive statistics are used to describe the basic features of the data in a study. They provide simple summaries about the sample and the measures. Together with simple graphics analysis, they form the basis of virtually every quantitative analysis of data.

Descriptive statistics are typically distinguished from inferential statistics. With descriptive statistics you are simply describing what is or what the data shows. With inferential statistics, you are trying to reach conclusions that extend beyond the immediate data alone. For instance, we use inferential statistics to try to infer from the sample data what the population might think. Or, we use inferential statistics to make judgments of the probability that an observed difference between groups is a dependable one or one that might have happened by chance in this study. Thus, we use inferential statistics to make inferences from our data to more general conditions; we use descriptive statistics simply to describe what's going on in our data.

Descriptive Statistics are used to present quantitative descriptions in a manageable form. In a research study we may have lots of measures. Or we may measure a large number of people on any measure. Descriptive statistics help us to simply large amounts of data in a sensible way. Each descriptive statistic reduces lots of data into a simpler summary. For instance, consider a simple number used to summarize how well a batter is performing in baseball, the batting average. This single number is simply the number of hits divided by the number of times at bat (reported to three significant digits). A batter who is hitting .333 is getting a hit one time in every three at bats. One batting .250 is hitting one time in four. The single number describes a large number of discrete events. Or, consider the scourge of many students, the Grade Point Average (GPA). This single number describes the general performance of a student across a potentially wide range of course experiences.

Every time you try to describe a large set of observations with a single indicator you run the risk of distorting the original data or losing important detail. The batting average doesn't tell you whether the batter is hitting home runs or singles. It doesn't tell whether she's been in a slump or on a streak. The GPA doesn't tell you whether the student was in difficult courses or easy ones, or whether they were courses in their major field or in other disciplines. Even given these limitations, descriptive statistics provide a powerful summary that may enable comparisons across people or other units.

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### Medical Statistics Part-I:Descriptive statistics

1. 1. Descriptive Statistics in cardiovascular research MOST SIMPLE WAY OF DATA HANDLING
2. 2. Statistics in general SUBCLAUSE USED FOR Collection Analysis  Interpretation Presentation  Reasoning  Discussion  Calculation  Scientific Inference
3. 3. STATISTICS IN GENERAL DESCRIPTIVE INFERENTIAL
4. 4. Descriptive Statistics  Data analysis begins with calculation of descriptive statistics for the research variables  These statistics summarize various aspects about the data, giving details about the sample and providing information about the population from which he sample was drawn  Each variable’s type determines the nature of descriptive statistics that one calculates and the manner in which one reports or displays those statistics  Simply to describe what's going on in our data
5. 5. inferential statistics  Trying to reach conclusions that extend beyond the immediate data alone=INFER  We use inferential statistics to try to infer from the sample data what the population might think/experience  Make judgments of the probability that an observed difference between groups is a dependable one or one that might have happened by chance in this study  Make inferences from our data to more general conditions http://www.socialresearchmethods.net/kb/statinf.php
6. 6. KEYWORDS  Population[Orientation]  SAMPLE[Representive]  VARIABLES[Characteristics]  PARAMETERS[quantities that define a statistical model]
7. 7. DISPLAY OF DESCRIPTIVE STATISTICS TABLES GRAGHS CHARTS CIRCLE DOT PLOTS BOX-AND-WHISKER PLOTS SCATTERPLOT SURVIVAL PLOTS BLAND-ALTMAN PLOTS
8. 8. TABLE-1
9. 9. Variables: DISCRETE CONTINUOUS  Only certain values (fixed and readily Countable  Examples of discrete variables commonly encountered in cardiovascular research include species, strain, racial/ethnic group, sex, education level, treatment group, hypertension status, and New York Heart Association class.  Infinite number of values  Fixed intervals between adjacent values  They can be manipulated mathematically, taking sums and differences  Age, height, weight, blood pressure, measures of cardiac structure and function, blood chemistries, and survival time
10. 10. Discrete variables (categorical) NOMINAL (UNORDERED) ORDINAL (ORDERED) Take values such as yes/no, Human/dog/mouse, female/male, treatment A/B/C; a nominal Variable that takes only 2 possible values is called binary. One May apply numbers as labels for nominal categories, but there Is no natural ordering Take naturally ordered values such as New York Heart Association class (I, II, III, or IV), hypertension status (optimal, normal, high-normal,or hypertensive), or education level (less than high school,high school, college, graduate school
11. 11. Categorical  A categorical variable (sometimes called a nominal variable) is one that has two or more categories, but there is no intrinsic ordering to the categories. For example, gender is a categorical variable having two categories (male and female) and there is no intrinsic ordering to the categories. Hair color is also a categorical variable having a number of categories (blonde, brown, brunette, red, etc.) and again, there is no agreed way to order these from highest to lowest. A purely categorical variable is one that simply allows you to assign categories but you cannot clearly order the variables. If the variable has a clear ordering, then that variable would be an ordinal variable, as described below.
12. 12. Ordinal  An ordinal variable is similar to a categorical variable. The difference between the two is that there is a clear ordering of the variables. For example, suppose you have a variable, economic status, with three categories (low, medium and high). In addition to being able to classify people into these three categories, you can order the categories as low, medium and high. Now consider a variable like educational experience (with values such as elementary school graduate, high school graduate, some college and college graduate). These also can be ordered as elementary school, high school, some college, and college graduate. Even though we can order these from lowest to highest, the spacing between the values may not be the same across the levels of the variables. Say we assign scores 1, 2, 3 and 4 to these four levels of educational experience and we compare the difference in education between categories one and two with the difference in educational experience between categories two and three, or the difference between categories three and four. The difference between categories one and two (elementary and high school) is probably much bigger than the difference between categories two and three (high school and some college).
13. 13. Ordinal  In this example, we can order the people in level of educational experience but the size of the difference between categories is inconsistent (because the spacing between categories one and two is bigger than categories two and three). If these categories were equally spaced, then the variable would be an interval variable
14. 14. Continuous variables  Continuous variables can have an infinite number of different values between two given points. As shown above, there cannot be a continuous scale of children within a family. If height were being measured though, the variables would be continuous as there are an unlimited number of possibilities even if only looking at between 1 and 1.1 meters.
15. 15. Descriptive statistics for Discrete variables  Absolute frequencies (raw counts) for each category  Relative frequencies (proportions or percentages of the total Number of observations)  Cumulative frequencies for successive categories of ordinal variables
16. 16. Collection  Formal Sampling  Recording Responses To Experimental Conditions  Observing A Process Repeatedly Over Time
17. 17. Descriptive statistics for continuous variables  Location statistics  MEAN  MEDIAN  MODE,  QUANTILES  Dispersion statistics[CENTRAL TENDENCY]  VARIANCE=  STANDARD DEVIATION=S=√S²  RANGE  INTERQUARTILE RANGE  Shape statistics  SKEWNESS  KURTOSIS
18. 18. ROBUST  MEDIAN is robust :Not strongly affected by outliers or by extreme changes to a small portion  MEAN is sensitive (not robust) to those conditions  MODE is robust to outliers, but it may be affected by data collection operations, such as rounding or digit preference, that alter data precision.
19. 19. QUANTILES  Quintiles combine aspects of ordered data and cumulative frequencies  The p-th quantile (0≤p≤1)  100p is an integer, the quantiles are called percentiles  Median, or 0.50 quantile, is the 50th percentile, the 0.99 quantile is the 99th percentile  Three specific percentiles are widely used in descriptive statistics, [100p is an integer multiple of 25]  Q1first quartile (25th percentile, 0.25 quantile)  Q2second quartile (50th percentile, 0.50 quantile), median  Q3third quartile (75th perce ntile,0.75 quantile)
20. 20. INTERQUARTILE RANGE[IQR]  It is a single number  defined as IQ of RQ-3Q1  Variance and standard deviation are affected (increased) by the presence of extreme observations, the IQR is not; it is robust
21. 21. SKEWNESS[skewness coefficient] For a given data  Distribution is symmetric (skewness=0)  A more pronounced tail in 1 direction than the  other (left tail, skewness<0; right tail, skewness>0)  If skewness=0, the mean= median  Right- (left-) skewed distribution has its mean value greater  (less than) the median
22. 22. Kurtosis  a measure of the “peakedness” of a distribution  A gaussian distribution (also called “normal”) with a bell-shaped frequency curve has kurtosis 0  Positive kurtosis indicates a sharper peak with longer/fatter tails and relatively more variability due to extreme deviations  Negative kurtosis coefficient indicates broader shoulders with shorter/thinner tails
23. 23. GRAPHS[complementary to tabular]
24. 24. DOT PLOT of Continuous variable(BMI) The dot plot is a simple graph that is used mainly with small data sets to show individual values of sample data in 1 dimension
25. 25. Box-and-whisker plot= box plot graph Graph displays values of quartiles (Q1, Q2, Q3) by a rectangular box. The ends of the box correspond to Q1 and Q3, such that the length of the box is the interquartile range (IQRQ3Q1). There is a line drawn inside the box at the median, Q2, and there is a “” symbol plotted at the mean.Traditionally, “whiskers” (thin lines) extend out to, at most,1.5 times the box length from both ends of the box: they connect all values outside the box that are not 1.5 IQR away from the box, and they must end at an observed value.Beyond the whiskers are outliers, identified individually by symbols such as circles or asterisks
26. 26. Univariate Analysis: Look one variable at a time for 3 features Distribution Central Tendency Dispersion Of Frequency in % /bar diagram/histogram Mean Median Mode Range Standard Deviation Variance
27. 27. Correlation[r] is a single 1 number that shows the degree of relationship between 2 variables -1 to +1
28. 28. r is also called Karl Pearson’s coefficient of correlation
29. 29. It is just beginning With best wishes